Compact third-order microstrip bandpass filter designed by the distributed- to lumped-element equivalence

In reality, it is not easy to design microstrip filters for the sake of distributed-element effect. It is an effective approach to approximate distributed-element structures through appropriate lumped-element circuits. In this paper, some basic microstrip structures are discussed, whose equivalent lumped-element circuits are derived. Then, a novel microstrip filter is obtained by connecting these microstrip structures, according to the similar topology of the third-order lumped-element bandpass filter. The equivalent lumped-element counterpart of the proposed microstrip filter clearly reveals its physical mechanism, ie, how the resonances are created and coupled and how the transmission zeros are created. Furthermore, a set of the design formulas are presented, which can be used to calculate initial structure parameters and then facilitate design process. The proposed microstrip bandpass filter can realize a third-order elliptic bandpass response with one transmission zero at each side of the passband. In addition, two short-circuited stubs are added to input/output ports to create the third transmission zero. The filter is featured by good frequency selectivity and out-of-band suppression. For demonstration, an actual example was designed, fabricated, and measured.